The present invention relates to methods for designing and manufacturing a rotationally symmetrical single-vision spectacle lens whose at least one of front and back surfaces is an aspherical surface, and a manufacturing system thereof.
Many spectacle lenses employ aspherical surfaces at one of front and back surfaces. When a spectacle lens employs an aspherical surface, the curvature becomes smaller while keeping a predetermined power as compared with a lens whose front and back surfaces are spherical, which decreases the maximum thickness of the lens.
When a rotationally symmetrical single-vision spectacle lens is designed, lens material and a vertex power are given as a specification. According to this specification and additional specification, a combination of shapes of front and back surfaces is found such that optical aberrations are minimized. The shape of the lens surface is calculated using an optimizing algorithm such as a damped least squares method. In the optimizing process, one or more (five or six, in general) lens parameters are selected as variables from among a plurality of lens parameters that define the spectacle lens, and values of optical aberration at evaluation points whose distances from the optical axis are different to one another are employed as evaluation functions.
The lens parameters include refractive index of the lens material, a diameter of the lens, a radius of curvature of the front surface, a radius of curvature of the back surface, a center thickness, a conic coefficient and high-order aspherical surface coefficients. A few lens parameters are selected to be variables. The refractive index and the diameter of lens are usually set as constants. The center thickness is set as a constant when a minus lens is designed, and it should be a variable to keep an appropriate edge thickness when a plus lens is designed. While both of the radii of curvatures of the front and back surfaces may be variables, one of them is set as a constant and the other is set as a variable in general. Since the conic coefficient is closely related to the high-order aspherical surface coefficients, the conic coefficient is set as a constant and the high-order aspherical surface coefficients are set as variables.
On the other hand, a vertex power can be employed as the evaluation function at the center of the lens. At each evaluation point, optical aberrations such as power error, astigmatism and distortion, and a performance according to the lens shape such as a thickness of the lens and the aspherical amount can be employed as the evaluation functions. The power error can be selected from among meridional power error, sagittal power error and average power error defined as average of the meridional and sagittal power errors.
The weighted square of difference between the value of the evaluation function and a desired target value is calculated for each of the evaluation points, the best possible combination of variables, where a merit function that is the total sum of the weighted square of differences is minimized, is found. In the damped least squares process, the best possible combination of variables is found while damping the variations of variables in consideration of nonlinearity of the system and dependence among the variables. Equality constraints may be defined for a few evaluation functions.
Since a single-vision spectacle lens is assumed to be used for various object distances, the optical performance should be balanced within a range of the object distance from 30 cm to infinity. Thus, in a conventional design method of a single-vision spectacle lens, the aberrations at the infinite and finite object distances are used as the evaluation functions at the same time, and the lens parameters are optimized such that the merit function containing these evaluation functions is minimized.
Two examples of the conventional design methods with the damped leased squares method will be described. FIGS. 27 to 30D show data and performance of a spectacle lens that is designed by a first conventional design method. In this example, a spherical power (SPH) is xe2x88x928.00 diopter, the front surface is spherical and the back surface is aspherical. A rotationally-symmetrical aspherical surface is expressed by the following equation:       X    ⁢          (      h      )        =                              h          2                ⁢        c                    1        +                              1            -                                          (                                  1                  +                  κ                                )                            ⁢                              h                2                            ⁢                              c                2                                                          +                  A        4            ⁢              h        4              +                  A        6            ⁢              h        6              +                  A        8            ⁢              h        8              +                  A        10            ⁢              h        10              +                  A        12            ⁢              h        12            ⁢      ⋯      
X(h) is a sag, that is, a distance of a curve from a tangential plane at a point on the surface where the height from the optical axis is h. Symbol c is a curvature (1/r) of the vertex of the surface, K is a conic coefficient, A4, A6, A8 and A10 are aspherical surface coefficients of fourth, sixth, eighth and tenth orders, respectively.
As shown in FIG. 27, the refractive index N, the lens diameter DIA, the radius of curvature R1 of the front surface, the radius of curvature R2 of the back surface, the center thickness CT, the conic coefficient xcexa and the high-order aspherical surface coefficients A4, A6, A8, A10 are the lens parameters. The parameters whose rightmost column xe2x80x9cVARIABLExe2x80x9d are checked by marks xe2x80x9cVxe2x80x9d are the variables. Namely, R2 and A4, A6, A8, A10 are set as variables and the other parameters are constants. The numerical values of the variables in the column xe2x80x9cVALUExe2x80x9d are the final values after optimization.
As shown in FIG. 28, the average power errors DAP and the astigmatisms AS at the infinite object distance on different evaluation points, and the average power errors DAP and the astigmatisms AS at the finite object distance xe2x88x92300 mm (the object distance takes minus value at a object side with respect to the lens) on the evaluation points are assigned to the evaluation functions as the optical aberrations, the vertex power AP at the lens center is added as the equality constraint. In the table of FIG. 28, xe2x80x9cVExe2x80x9d denotes the evaluation function, xe2x80x9cODxe2x80x9d denotes the object distance, xe2x80x9chxe2x80x9d denotes the distance of the evaluation point from the optical axis and xe2x80x9cTVxe2x80x9d denotes the target value. The twenty evaluation points whose distances from the optical axis are different to one another are set on the lens surface. The center evaluation point is on the optical axis (the distance is 0 mm) and the distance of the farthest evaluation point is 40 mm. The interval of the evaluation points is 2 mm. The total number of the evaluation functions is 81 because four kinds of the optical aberration at the twenty evaluation points and the vertex power AP are employed. The target values of the evaluation functions regarding the optical aberration are zero. The target value of the evaluation function regarding the vertex power is set as xe2x88x928.00. As shown by the values in the column xe2x80x9cWEIGHTxe2x80x9d of FIG. 28, evaluated values, which are the differences between the values of the evaluation functions and the target values, are weighted such that the weight decreases with the distance from the optical axis, and the variables are optimized using the damped least squares method.
FIGS. 29A-29D are graphs showing the optical aberrations of the optimized spectacle lens of the first conventional design with respect to a visual angle xcex2 (unit: degrees) as the vertical axis; FIG. 29A shows the meridional power error DM, FIG. 29B shows the sagittal power error DS, FIG. 29C shows the average power error DAP and FIG. 29D shows the astigmatism AS. The solid line represents the aberration when the object visual diopter, which is a reciprocal of the object distance (unit: m), is 0 D (equivalent to the infinite object distance), the long dashed line represents the aberration when the object visual diopter is xe2x88x922 D (the object distance xe2x88x92500 mm) and the short dashed line represents the aberration when the object visual diopter is xe2x88x924 D (the object distance xe2x88x92250 mm).
Further, FIGS. 30A-30D are graphs showing the optical aberrations of the optimized spectacle lens of the first conventional design with respect to the object visual diopter DO (unit: D) as the vertical axis; FIG. 30A shows the meridional power error DM, FIG. 30B shows the sagittal power error DS, FIG. 30C shows the average power error DAP and FIG. 30D shows the astigmatism AS. The solid line represents the aberration when the visual angle is 20 degrees, the long dashed line represents the aberration when the visual angle is 30 degrees and the short dashed line represents the aberration when the visual angle is 40 degrees.
FIGS. 29A-29D show that the various aberrations vary undulately but not monotonously with respect to the change of the visual angle xcex2. FIGS. 30A-30D show that the object visual diopter for the minimum aberration varies depending on the visual angle and that the far-and-near balance varies depending on the visual angle xcex2.
FIGS. 31 to 34D show data and performance of a spectacle lens that is designed by a second conventional design method. In this example, a spherical power (SPH) is +6.00 diopter, the front surface is aspherical and the back surface is spherical. The sort of the lens parameters is the same as the first conventional design method. The parameters whose rightmost column xe2x80x9cVARIABLExe2x80x9d are checked by marks xe2x80x9cVxe2x80x9d are the variables. Namely, the radius of curvature R2 of the back surface, the center thickness CT and the high-order aspherical surface coefficients A4, A6, A8, A10 are set as variables and the other parameters are constants.
As shown in FIG. 32, the average power errors DAP and the astigmatisms AS at the infinite and finite (xe2x88x92300 mm) object distances on the evaluation points are assigned to the evaluation functions as the optical aberrations, the vertex power AP and the edge thickness T are added as the equality constraints. The total number of the evaluation functions is 82. The evaluated values are weighted in the same manner as the first conventional design method, and the variables are optimized using the damped least squares method.
FIGS. 33A-33D are graphs showing the optical aberrations of the optimized spectacle lens of the second conventional design with respect to the visual angle xcex2 (unit: degrees) as the vertical axis. FIGS. 34A-34D are graphs showing the optical aberrations of the optimized spectacle lens of the second conventional design with respect to the object visual diopter DO (unit: D) as the vertical axis. These graphs show that the various aberrations undulate with respect to the visual angle xcex2 and that the far-and-near balance varies depending on the visual angle xcex2.
As described above, since the conventional design methods employ a great number of the evaluation functions, the cost of calculation becomes large and the far-and-near balance varies depending on the visual angle xcex2.
Further, since it is impossible to take all of the evaluation functions as zero in theory and the aberration undulates with respect to the visual angle xcex2 when the weighting is constant, an operator is required to control the weighting to direct the aberrations toward the desired target values. This increases labor cost, and the optimized results for the same specification may be different according to the operators.
Still further, in the conventional design methods, since there are a great number of the evaluation functions, the variation of the merit function is exceedingly complex. As a result, there is the potential that the merit function is trapped in local minimum. That is, there is a high possibility that the optimizing is stopped at the local minimum that is not true minimum. In order to avoid trapping, the operator must monitor the condition of the optimization.
Such an intervention of the operator presents no problem when a single-vision spectacle lens is designed as a ready-made article within a range of manufacturing. However, when a single-vision spectacle lens is designed as a custom-made article, since the lens having the optimum optical performance should be designed based on various special orders such as a curve, a diameter, a lens type and a shape balance between right and left lenses, which are designated by a customer, the intervention of the operator presents problem from viewpoints of the cost and the design repeatability. That is, the same result is not always obtained based on the same specification.
It is therefore an object of the present invention to provide a design method of a spectacle lens, which is capable of finding the most suitable solution in short time without an operator and of reducing the variation of the far-and-near balance depending on the visual angle. Further object of the present invention is to provide manufacturing method and system employing the design method.
For the above object, according to the present invention, there is provided an improved design method of a spectacle lens, which includes step for selecting one or more lens parameters as variables among a plurality of lens parameters, step for assigning values of the same optical aberration at different evaluation points on the lens to all of evaluation functions that evaluate optical aberration and step for optimizing the selected lens parameters by setting target values of the evaluation functions to zero. In general, there are a great number of evaluation functions including the equality constraints. The evaluation function may evaluate optical aberration or a lens parameter. In the present invention, the evaluation functions that evaluate the optical aberration are defined as the values of the same optical aberration at the different evaluation points. Since the lens parameter is usually employed as the equality constraint, the assigning step may be defined to select values of only one optical aberration for the evaluation functions except equality constraints.
The optimizing step includes repetition of step for calculating the magnitudes of the evaluation functions and step for adjusting the values of the selected lens parameters such that the evaluation functions are closer to zero. That is, the values of the selected lens parameters are adjusted such that the merit function, which is the total sum of the weighted square of the differences between the evaluation functions and the target values, is minimized.
With this method, the small number of the evaluation functions reduces the cost of calculation and it is possible to take all of the final values of the evaluation functions regarding the optical aberration as zero. Therefore, it is unnecessary that an operator intervenes to control the weighting and to monitor the condition of the optimization, which reduces the labor cost and keeps the design repeatability. Further, the variation of the far-and-near balance depending on the visual angle can be reduced in spite of assigning the values of the same optical aberration to all of the evaluation functions.
The optical aberration employed as the evaluation function can be selected from among meridional power error, sagittal power error and aberration defined as a weighted sum thereof. As shown in FIGS. 30A-30D and FIGS. 34A-34D for the conventional design methods, the meridional power error DM, the sagittal power error DS, the average power error DAP and the astigmatism AS vary linearly with respect to the object visual diopter. Further, the following relationships are held at the specific visual angle.
DM≈Axc3x97DO+B
DS≈C
DAP=(DM+DS)/2≈A/2xc3x97DO+(B+C)/2
AS=DMxe2x88x92DS≈Axc3x97DO+(Bxe2x88x92C)
Where A, B and C are constants.
The slope A of the straight line indicating the meridional power error DM depends on the base curve of the lens and it does not vary regardless of the small change of the aspherical surface. The sagittal power error DS is almost constant regardless of the object distance. Accordingly, if the optical aberrations DM, DS, DAP and AS, which are closely related to one another, are employed as the evaluation functions at the same time, it only increases in complexity of the merit function but does not increase the efficiency of the optimization. On the contrary, when the optical aberration is limited to one of the meridional power error DM, the average power error DAP that is found by 0.5xc3x97DM+0.5xc3x97DS, the astigmatism AS that is found by DM+(xe2x88x921)xc3x97DS, the better result can be obtained in both of the calculation cost and the optical performance.
When the values of any one of the meridional power error, the average power error or the astigmatism are selected as the evaluation functions of the optimization, the solution where all of the evaluation functions become zero can be found by selecting a specific object distance (including a virtual distance at the side of an eye with respect to the lens). Therefore, when the object distance is properly selected and the target values of the evaluation functions are set as zero, the merit function reaches the most suitable solution with stability and the judgement of convergence of the optimization becomes easier. The evaluation functions may be the values of the optical aberration at a specific object distance or the calculated results of the values of the optical aberration at different object distances. In the later case, the evaluation functions may be averages of the values of the astigmatism at the two specific object distances. The object distances maybe infinity and xe2x88x92300 mm, for example.
In the optimizing step, either a least squares method or a damped least squares method can be employed as an optimizing algorithm. Equality constraints may be included in the optimizing. At least one of the minimum lens thickness and the vertex power may be included as the equality constraints. The vertex power may be adjusted by means of bending in place of the addition of the equality constraints.
On the other hand, the manufacturing method of the spectacle lens according to the invention includes step for selecting one or more lens parameters as variables among a plurality of lens parameters, step for assigning values of the same optical aberration at different evaluation points on the lens to all of evaluation functions, step for optimizing the selected lens parameters by setting target values of the evaluation functions to zero based on ordering data, step for calculating manufacturing data from the optimized lens parameters, and step for processing a refractive surface of the lens according to the manufacturing data. The optimizing step includes repetition of step for calculating the magnitudes of the evaluation functions and step for adjusting the values of the selected lens parameters such that the evaluation functions are closer to zero.
Further, the manufacturing system of the spectacle lens according to the invention includes an input device that is used for inputting ordering data that defines a specification of a spectacle lens, a calculating device that calculates an optimum lens shape from the ordering data, and a processing device that processes the lens based on the optimum lens shape. The calculating device selects one or more lens parameters as variables among a plurality of lens parameters and assigns values of the same optical aberration at different evaluation points on the lens to all of evaluation functions, and the calculating device optimizes the selected lens parameters by evaluating the evaluation functions.